Problem: You are given three integers a, b, k.

Find two binary integers x and y (x ≥ y) such that 

  1. both x and y consist of a zeroes and b ones; 
  2. x - y (also written in binary form) has exactly k ones. 

You are not allowed to use leading zeros for x and y. 

Input

The only line contains three integers a, b, and k (0 ≤ a; 1 ≤ b; 0 ≤ k ≤ a + b ≤ 2 ⋅ 10^5) — the number of zeroes, ones, and the number of ones in the result.

Output

If it's possible to find two suitable integers, print "Yes" followed by x and y in base-2.

Otherwise print "No".

If there are multiple possible answers, print any of them.

Examples

Input


4 2 3


Output


Yes
101000
100001


Input


3 2 1


Output


Yes
10100
10010


Input


3 2 5


Output


No

Note

In the first example, x = 101000_2 = 2^5 + 2^3 = 40_{10}, y = 100001_2 = 2^5 + 2^0 = 33_{10}, 40_{10} - 33_{10} = 7_{10} = 2^2 + 2^1 + 2^0 = 111_{2}. Hence x-y has 3 ones in base-2.

In the second example, x = 10100_2 = 2^4 + 2^2 = 20_{10}, y = 10010_2 = 2^4 + 2^1 = 18, x - y = 20 - 18 = 2_{10} = 10_{2}. This is precisely one 1.

In the third example, one may show, that it's impossible to find an answer.

Solution (in PYTHON3):

Solution:
from sys import stdin, stdout 
input = stdin.readline
 
a,b,k = map(int,input().split())

if k==0:
    s1 = '1'*b + '0'*a
    s2 = '1'*b + '0'*a
    a=0
    b=0
else:
    s1 = '1'
    s2 = '1'
    b-=1
    
    if a<k and a>0:
        # print(a,b,k)
        # print('AAA')
        s = '1'*(k-a) + '0'*(a-1)
        s1 += '1' + s + '0'
        s2 += '0' + s + '1'
        b -= ((k-a) + 1)
        a = 0
    else:
        s1 += '1' + ('0'*k)
        s2 += ('0'*k) + '1'
        b -= 1
        a -= k
    
    if b>0:
        s1 += '1'*b
        s2 += '1'*b
    if a>0:
        s1 += '0'*a
        s2 += '0'*a
# print(a,b)
if a<0 or b<0:
    print('NO')
else:
    print('YES')
    print(s1)
    print(s2)